Source code for colour.colorimetry.blackbody

#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
Blackbody - Planckian Radiator
==============================

Defines objects to compute the spectral radiance of a planckian radiator and
its spectral power distribution.

See Also
--------
`Blackbody Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/colorimetry/blackbody.ipynb>`_
"""

from __future__ import division, unicode_literals

import numpy as np

from colour.colorimetry import (
    DEFAULT_SPECTRAL_SHAPE,
    SpectralPowerDistribution)

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2017 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = '[email protected]'
__status__ = 'Production'

__all__ = ['C1',
           'C2',
           'N',
           'planck_law',
           'blackbody_spectral_radiance',
           'blackbody_spd']

C1 = 3.741771e-16  # 2 * math.pi * PLANCK_CONSTANT * LIGHT_SPEED ** 2
C2 = 1.4388e-2  # PLANCK_CONSTANT * LIGHT_SPEED / BOLTZMANN_CONSTANT
N = 1


[docs]def planck_law(wavelength, temperature, c1=C1, c2=C2, n=N): """ Returns the spectral radiance of a blackbody at thermodynamic temperature :math:`T[K]` in a medium having index of refraction :math:`n`. Parameters ---------- wavelength : numeric or array_like Wavelength in meters. temperature : numeric or array_like Temperature :math:`T[K]` in kelvin degrees. c1 : numeric or array_like, optional The official value of :math:`c1` is provided by the Committee on Data for Science and Technology (CODATA) and is :math:`c1=3,741771x10.16\ W/m_2` *(Mohr and Taylor, 2000)*. c2 : numeric or array_like, optional Since :math:`T` is measured on the International Temperature Scale, the value of :math:`c2` used in colorimetry should follow that adopted in the current International Temperature Scale (ITS-90) *(Preston-Thomas, 1990; Mielenz et aI., 1991)*, namely :math:`c2=1,4388x10.2\ m/K`. n : numeric or array_like, optional Medium index of refraction. For dry air at 15°C and 101 325 Pa, containing 0,03 percent by volume of carbon dioxide, it is approximately 1,00028 throughout the visible region although *CIE 15:2004* recommends using :math:`n=1`. Returns ------- numeric or ndarray Radiance in *watts per steradian per square metre*. Notes ----- - The following form implementation is expressed in term of wavelength. - The SI unit of radiance is *watts per steradian per square metre*. References ---------- .. [1] CIE TC 1-48. (2004). APPENDIX E. INFORMATION ON THE USE OF PLANCK’S EQUATION FOR STANDARD AIR. In CIE 015:2004 Colorimetry, 3rd Edition (pp. 77–82). ISBN:978-3-901-90633-6 Examples -------- >>> # Doctests ellipsis for Python 2.x compatibility. >>> planck_law(500 * 1e-9, 5500) # doctest: +ELLIPSIS 20472701909806.5... """ l = np.asarray(wavelength) t = np.asarray(temperature) p = (((c1 * n ** -2 * l ** -5) / np.pi) * (np.exp(c2 / (n * l * t)) - 1) ** -1) return p
blackbody_spectral_radiance = planck_law
[docs]def blackbody_spd(temperature, shape=DEFAULT_SPECTRAL_SHAPE, c1=C1, c2=C2, n=N): """ Returns the spectral power distribution of the planckian radiator for given temperature :math:`T[K]`. Parameters ---------- temperature : numeric Temperature :math:`T[K]` in kelvin degrees. shape : SpectralShape, optional Spectral shape used to create the spectral power distribution of the planckian radiator. c1 : numeric, optional The official value of :math:`c1` is provided by the Committee on Data for Science and Technology (CODATA) and is :math:`c1=3,741771x10.16\ W/m_2` *(Mohr and Taylor, 2000)*. c2 : numeric, optional Since :math:`T` is measured on the International Temperature Scale, the value of :math:`c2` used in colorimetry should follow that adopted in the current International Temperature Scale (ITS-90) *(Preston-Thomas, 1990; Mielenz et aI., 1991)*, namely :math:`c2=1,4388x10.2\ m/K`. n : numeric, optional Medium index of refraction. For dry air at 15°C and 101 325 Pa, containing 0,03 percent by volume of carbon dioxide, it is approximately 1,00028 throughout the visible region although *CIE 15:2004* recommends using :math:`n=1`. Returns ------- SpectralPowerDistribution Blackbody spectral power distribution. Examples -------- >>> from colour import STANDARD_OBSERVERS_CMFS >>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> print(blackbody_spd(5000, cmfs.shape)) SpectralPowerDistribution('5000K Blackbody', (360.0, 830.0, 1.0)) """ wavelengths = shape.range() return SpectralPowerDistribution( name='{0}K Blackbody'.format(temperature), data=dict( zip(wavelengths, planck_law( wavelengths * 1e-9, temperature, c1, c2, n))))